Sum of infinitesimal rotations around different points in 2D space ?

in order to numerically solve a physics problem I think I need to add 2 (infinitesimal) rotations of one and the same segment each around a different point in 2D space in one iteration of numeric approximization. How does this addition work out? Is it the sum of the vectors connecting the startpoint of each rotation with its endpoint? I don't find a conclusive solution.